Recent content by jonathan_lam

So the exam is tomorrow but I can't afford a calculator. Do I really need one? Most of the mathematics in the course does not require a calculator as they are proof based/involve pronumerals rather than actual numbers. For example, graphing would not require much use of a calculator, and conics...

Reminds me of https://www.research.ibm.com/haifa/ponderthis/challenges/May2001.html and https://www.research.ibm.com/haifa/ponderthis/solutions/May2001.html (spoiler alert - solutions are in the second link)

I just checked the textbook and I typed the question wrong. There should be a square in the denominator but not inside the log. This might be what OP is asking?

There is a similar question in a Sydney Grammar textbook: \int_0^1\frac{\log(1+x)}{1+x^2}. It also appeared in a Putnam a long time ago. Use the substitution x=\tan\theta so I= \int_0^{\frac{\pi}{4}} \log(1+\tan\theta) \, d\theta Use the fact that \int_0^a f(x) =\int_0^a f(a-x) so I =...

I did all four. Anyone is allowed to participate in the olympiad, but only year 10 and 11 (and I think year 9 if they are old enough) are eligible for the summer school. Also offers have been sent out for quite a while now (since last week).

\int x^2 e^x \,dx and \int x^2\cos x \,dx and \int (\log x)^2\,dx are also examples. Whether they have been asked before, I'm not too sure. I can't be bothered checking through all the past papers.

Isn't that called reduction formula?

I got the question from David Monk, who wrote a book with geometry questions. I decided to chuck it in the trial, without solutions. Alternate solutions involving other parametrisations or complex numbers or just euclidean geometry would be interesting as well.

Actually it was EES 5% and it wasn't even a serious attempt. Just writing random answers and leaving half the exam blank. For all those 8 markers, I wrote 3 sentences.

You'll have to find out from your school - so ask your teacher/head teacher/olympiad coordinator.

I got a call this morning offering me a place at the summer school. But I had to decline because I'm in year 12.

Hello, I keep getting stuck on this question. It gets a bit messy. I already did part (a) - the point A (and hence B,C,D) all lie on the circle given... just parts b, c, d I need.

median was like 87 or something

Most people got like 90+ We also didn't cover mechanics and volumes at the time of the exam rip

spud is that you?